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An alternative approach to structure specification based on fuzzy multidimensional membership function using forward selection rule
* 1 , 2 , 3 , 4
1  Assistant Professor, The Bhawanipur Education Society College,Calcutta University
2  Department of Mathematics, Vidyasagar Evening College and Guest Faculty Department of Atmospheric Science, Calcutta University
3  Department of Mathematics, J.U.
4  Assistant Professor, Academy of Technology, Kolkata



 Fuzzy logic first established in July,1964 by Lofti A.  Zadeh, is usually used to develop cost-effective approximate solutions to complex real-world problems exploiting the tolerance of imprecision.

The present study attempts to develop a general computational technique based on fuzzy multi-dimensional membership function using forward selection rule for discriminating two different situations which is basically non-linear. Incidentally the technique suggested here is validated with atmospheric data.

Earlier the fundamental principal component analysis (PCA) technique was applied to identify the significant parameters for the occurrence of pre-monsoon thunderstorms (TS) in Kolkata. They showed how the linear discriminant analysis (LDA) technique alone as well as in conjunction with PCA can be successfully applied for the purpose (Ghosh et al. 1999, 2004; Chatterjee et al., 2009). Also a comparative study was performed between the existing multivariate technique, the linear discriminant analysis and a technique based on fuzzy membership roster method (Chatterjee et al., 2011). Recently a fuzzy –neuro based algorithm for weather prediction has been developed (T. Rahman et al. 2014).

 The main objective of the study is to address the numerical imprecision of some quantified physical variables. In this rule, a product form is taken to construct the multivariate membership function where the univariate membership function is Gaussian in nature as well as continuously differentiable. Since the parameters may have different units so they are made dimensionless before taking the product. To develop the technique no software package or fuzzy toolbox is used. The program for the study is developed by the authors themselves.  

This rule is applied to two datasets of different categories consisting of the parameters of the days with convective development and fair weather respectively during pre-monsoon season of Kolkata (22.53ºN, 88.33ºE), India. Basic parameters for discriminating the situation (convective development and fair weather in pre-monsoon season of Kolkata) is constructed from the known data set of 12 years covering the period 1985-1996. The results are validated for the period 1997-1999 using the dataset consisting of variables of unknown nature. The study reveals that the technique can classify the two different situation to give the best possible combination of parameters with atmost 88% success rate. Moreover, the study indicates that the two datasets are structurally different.

The technique suggested here is expected to work in any other domain too. It is found that the method works with better accuracy than the existing ones so far the atmospheric parameters are concerned. The detail will be discussed in the literature.